Digital Pre-Distortion Derek Kozel What is Digital Pre-Distortion - - PowerPoint PPT Presentation

Digital Pre-Distortion

Derek Kozel

What is Digital Pre-Distortion (DPD)

• A technique for improving the linearity of power amplifiers
• Ideally the output signal of a PA is the input scaled up perfectly
• Instead the semiconductor physics causes distortions

○ Amplitude, frequency, and phase errors

• If we can predict the errors, we can try to reverse them

keysight.com

High Level Flow

https://www.analog.com/en/analog-dialogue/articles/ultrawideband-digital-predistortion-rewards-and-challenge-of-implementation-in-cable-system.html

Why use DPD?

• Want to get as much power out of an amplifier as possible

○ Start getting close to limits of the device ○ Output power starts compressing ■ 1 dB increase in input -> < 1 dB increase in output ○ Output signal now a distorted version of the input!

• PA efficiency best when driven near saturation

www.electronicdesign.com/

Background Transistor Theory

Ideal Field Effect Transistor

• Voltage controlled current source
• Three terminals (connections)

○ Gate: “control port” ○ Drain and Source: variable resistor

• Changing the voltage across these terminals

changes the resistance between Drain and Source and thus the current flowing

bradysalz.com/technical/the-mosfet/

FET as an amplifier

• Usually the Gate to Source voltage is the input
• Voltage at the Drain is the output

electronicspost.com/mosfet-amplifier/

IV Curve and Load-Line

• Shows how much does current

change for a given change in Gate to Source voltage

• Load line shows the path the

amplifier ideally operates on

• Looks mostly linear, but rounds off

at the extremes of the load line

Distortion

Ideal Transfer Function

• Ideally an amplifier’s output voltage (across some load impedance) is:
• Where a is the voltage gain of the amplifier

Two Tone Test Setup

Ideal Two Tone Result

Non-Linear Transfer Function

• What the output actually looks like can be modelled using a Volterra series

polynomial

• We see the linear gain, a1, and additional terms for higher order distortion
• This is only a behavioral model, it does not try to simulate the circuit
• Output only depends on current input value

Second Order Distortion

• The polynomial has terms for both odd and even degree terms
• Lets look at what happens when a tone is squared
• The result is a tone at twice the original frequency!

Third Order Distortion

• Now what about cubed?
• The output has energy at both the original frequency and third harmonic!
• Interesting takeaway:

○ Even order distortion does not cause tones near the fundamental ○ Odd order distortion does

Simplified Volterra Series

• Let us assume that we only care about distortion resulting in signals near our

fundamental

○ Only include odd power terms

• For completeness, here’s the 5th order expansion

○ Note that there is energy at the first, third, and fifth harmonics!

Two Tone Distortion

• Input signal:
• Results in In-Band distortion

○ Third order distortion will cause:

• Takeaways

○ Fundamental tone will be distorted by all odd power non-linearity ○ Sum and difference tones have energy from all higher order non-linearities

Two Tone Distortion

Advanced Techniques in RF Power Amplifier Design (S. C. Cripps)

Non-Linear Two Tone Test

Determining Coefficients

• Now we have an equation that I assert models the behavior of a PA

reasonably well

• Need to determine the coefficients for a particular PA
• Common approach:

○ Use a single tone test signal and sweep input power range ○ Measure output power (AM-AM plot) ○ Use Least Mean Squares algorithm to estimate the coefficients

… And Phase too

• Power amplifiers also distort phase
• The Volterra series can be expanded by making the coefficients complex

Pre-Distortion

Pre-Distortion

• Need to increase the input power to account for the distortion
• Can only increase to the limit of the input driver

○ Total dynamic range decreased, but is now more linear

http://edadocs.software.keysight.com/display/ads2009/Theory+of+Operation+for+Digital+Predistortion

Inverting the Transfer Function

• Possible to do algebraically, but the equations become lengthy quickly

○ Direct Learning method

• Most frequently an optimization loop is used

○ Algorithmically vary the coefficients while measuring PA output distortion ○ Least Mean Squares, Recursive Mean Squares, others ○ Indirect Learning

“A SiGe PA With Dual Dynamic Bias Control and Memoryless Digital Predistortion for WCDMA Handset Applications”

GNU Radio Blocks

Full band DPD

• Uses Recursive Least Squares to find coefficients
• Written by Srikanth Pagadarai

○ Published in 2016 IEEE 83rd Vehicular Technology Conference ■ Srikanth Pagadarai ; Rohan Grover ; Samuel J. Macmullan ; Alexander M. Wyglinski ○ “Digital Predistortion of Power Amplifiers for Spectrally Agile Wireless Transmitters” ○ GNU Radio assistance by Travis Collins

• https://github.com/SrikanthPagadarai/gr-dpd
• Includes OFDM test code

Sub Band DPD

• Can isolate and compensate for a single intermodulation product
• Developed by Chance Tarver and Mahmoud Abdelaziz

○ Published in 2017 IEEE International Symposium on Circuits and Systems ■ Chance Tarver ; Mahmoud Abdelaziz ; Lauri Anttila ; Joseph R. Cavallaro ○ “Multi component carrier, sub-band DPD and GNURadio implementation”

• Uses a memoryless polynomial
• Includes the volterra series PA model used in the examples today
• Also indirect learning model

Future Plans

• Merge existing code into single OOT module

○ Authors of both existing modules supportive and able to help

• Adapt testbenches to use standard GNU Radio OFDM blocks

○ Increase flexibility, demonstrate full TX->RX impact

• Add documentation
• Add implementations of memory polynomials

○ Thermal and capacitive effects mean the output is not only dependant on the current input

• Possible Google Summer of Code project

○ Already some interested students

Thanks and Questions?

The latest version of these slides can be found at www.derekkozel.com/talks @derekkozel @dkozel@social.coop